Subject:
Mathematics
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Mathematics, Tmm0022
Language:
English
Media Formats:
Text/HTML

# Trigonometric Identities, Sum and Difference Formulas and Applications

## Overview

TMM 002 PRECALCULUS (Revised March 21, 2017)

4.  Equivalencies:

4c. Become fluent with conversions using traditional equivalency families.*

• The student can prove trigonometric identies.
• The student solves trigonometric equations.

# Trigonometric Identities and Formulas

Formulas introduced in this chapter seem to be many but all of them are derived from the fundamental identities and the sum/difference formulas. It would be very helpful for students if they strive to derive the double-angle, half-angle, etc., formulas from the sum/difference formulas. Proving other identities is a challenge but is an important exercise. This can be supplemented by assigning problems of computing trigonometric ratios of certain angles. For example, finding the value of COS(3.75°) which requires repeated use of half-angle formula or finding $$\sin^{4}(\pi/16)$$ which requires power-reduction.

In this module, we use the fundamental identities to derive important formulas for the six trigonometric functions which are quite useful in calculus.

Review: Fundamental trigonometric identities and the Pythagorean Theorem

Learning Objectives:

• Even – Odd Identitites
• Cofunction Identities
• Sum and Difference Formulas
• Double Angle Formulas
• Half-Angle Formulas
• Power Reduction formulas
• Product to Sum and Sum to Product Formulas